Aptitude Discussion

Q. |
What is the remainder left after dividing $1!+2!+3!.....+100!$ by $7$? |

✖ A. |
0 |

✔ B. |
5 |

✖ C. |
14 |

✖ D. |
21 |

**Solution:**

Option(**B**) is correct

$7!+8!+9!.......+100!$ is completely divisible by $7$.

Now, $1!+2!+3!....+6! = 873$

When $873$ is divided by $7$ it leaves a remainder $= \textbf{5}.$

**Poonam Pipaliya**

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u can take 7! common.

7x6x5x4x3x2x1( 8+9x8+ 10x9x8 + and so on....) will always be divisible by 7.

sir how can you say that 7!+8!+.....+100! is completely divided by 7...??..!!please elaborate it.